Carol Danvers was the original female superheroine to use the name Captain Marvel.
Her first appearance was not as Captain Marvel but as Carol Danvers in Marvel Super-heroes #13 – Mar 1968. She was a regular Air Force pilot. The original character (Carol Danvers) was designed to be the female counterpart to Captain Marvel (Kree hero). Carol was a normal human Air Force officer that was caught in an explosion with the Kree super-hero Captain Marvel (Captain Marvel #18 – Nov 1969). As a result of the explosion her DNA was merged with Captain Marvel and she reappeared in Ms. Marvel #1 (Jan 1977). Carol Danvers joined the Avengers one year later (Avengers #171- May 1978).
It was later she joined the X-men and the much later the Star Jammers calling herself Binary after she was experimented on the brood giving her energy wielding abilities.
In later comics she returns to the Avengers under a new name – Warbird.
Carol later resumes using the name Captain Marvel in July 2012 after a discusion with Captain America wherein he convinces her to Honor the original kree super-hero captain Marvel.